Finite Group Databasebeta

← #13074890

Subgroups — #13074890

Order 1408.

562 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#67000C211yesmaximal, characteristic
2C2×#66997C211yesmaximal, characteristic, complemented
3C2×#66949C211yesmaximal, characteristic, complemented
4C2×#66947C211yesmaximal, characteristic
5C11×#395C211yesmaximal, characteristic, complemented
6#10622605C211yesmaximal, characteristic, complemented
7#10622603C211yesmaximal, characteristic, complemented
8#10622602C211yesmaximal, characteristic, complemented
9#10622585C211yesmaximal, characteristic, complemented
10#10622289C211yesmaximal, characteristic, complemented
11#10622288C211yesmaximal, characteristic, complemented
12#10622286C211yesmaximal, characteristic, complemented
13#10622285C211yesmaximal, characteristic
14#10622282C211yesmaximal, characteristic, complemented
15#10622265C211yesmaximal, characteristic, complemented
16C22×Q8×C11C2211yescharacteristic
17C22×D44C2211yescharacteristic
18C22×C4×D11C2211yescharacteristic
19C22×Dic22C2211yescharacteristic
20C2×C11×C4⋊C4C2211yescharacteristic
21C2×C11×C4⋊C4C2211yescharacteristic
22C2×C11×C4⋊C4C2211yescharacteristic
23#67000—24no—
24#66997—24no—
25C2×(C2×D11)⋊C4C2211yescharacteristic
26C2×(C2×D11)⋊C4C2211yescharacteristic
27C2×(C2×D11)⋊C4C2211yescharacteristic
28C2×(C2×D11)⋊C4C2211yescharacteristic
29C2×(C2×D11)⋊C4C2211yescharacteristic
30C2×(C2×D11)⋊C4C2211yescharacteristic
31C2×(C2×D11)⋊C4C2211yescharacteristic
32C2×(C2×D11)⋊C4C2211yescharacteristic
33C2×(C2×D11)⋊C4C2211yescharacteristic
34C2×(C2×D11)⋊C4C2211yescharacteristic
35C2×(C2×D11)⋊C4C2211yescharacteristic
36C2×Dic11⋊C4C2211yescharacteristic
37C2×Dic11⋊C4C2211yescharacteristic
38C2×Dic11⋊C4C2211yescharacteristic
39C2×Dic11⋊C4C2211yescharacteristic
40C2×Dic11⋊C4C2211yescharacteristic
41C2×Dic11⋊C4C2211yescharacteristic
42C2×Dic11⋊C4C2211yescharacteristic
43C2×C4×Dic11C2211yescharacteristic
44C2×C4×Dic11C2211yescharacteristic
45#66949—24no—
46#66947—24no—
47C11×#95C2211yescharacteristic
48C11×#95C2211yescharacteristic
49C11×#95C2211yescharacteristic
50C11⋊#95C2211yescharacteristic
51C11⋊#95C2211yescharacteristic
52C11⋊#95C2211yescharacteristic
53C11⋊#95C2211yescharacteristic
54C11⋊#95C2211yescharacteristic
55C23×D11C2311yescharacteristic
56C23×D11C2311yescharacteristic
57C2×Q8×C11—22no—
58C2×Q8×C11—22no—
59C2×Q8×C11—41no—
60C22×C4×C11C2311yescharacteristic
61C22×C4×C11C2311yescharacteristic
62C22×C4×C11C2311yescharacteristic
63C22×C4×C11C2311yescharacteristic
64C22×C4×C11C2311yescharacteristic
65C22×C4×C11C2311yescharacteristic
66C22×C4×C11C2311yescharacteristic
67C22×Dic11C2311yescharacteristic
68C22×Dic11C2311yescharacteristic
69C22×Dic11C2311yescharacteristic
70C22×Dic11C2311yescharacteristic
71C22×Dic11C2311yescharacteristic
72C22×Dic11C2311yescharacteristic
73C2×D44—22no—
74C2×D44—22no—
75C2×D44—41no—
76C2×C4×D11—22no—
77C2×C4×D11—22no—
78C2×C4×D11—41no—
79C2×Dic22—22no—
80C2×Dic22—22no—
81C2×Dic22—41no—
82C11×C4⋊C4—22no—
83C11×C4⋊C4—22no—
84C11×C4⋊C4—41no—
85(C2×D11)⋊C4—22no—
86(C2×D11)⋊C4—22no—
87(C2×D11)⋊C4—22no—
88(C2×D11)⋊C4—22no—
89(C2×D11)⋊C4—22no—
90(C2×D11)⋊C4—22no—
91(C2×D11)⋊C4—22no—
92(C2×D11)⋊C4—22no—
93(C2×D11)⋊C4—22no—
94(C2×D11)⋊C4—41no—
95(C2×D11)⋊C4D414yes—
96Dic11⋊C4—22no—
97Dic11⋊C4—22no—
98Dic11⋊C4—22no—
99Dic11⋊C4—22no—
100Dic11⋊C4—22no—
101Dic11⋊C4—22no—
102Dic11⋊C4D414yes—
103C4×Dic11—22no—
104C4×Dic11—22no—
105#2674—111nomaximal, Sylow
106C23×C11C2411yescharacteristic
107C22×D11—21no—
108C22×D11—21no—
109C22×D11—21no—
110C22×D11—21no—
111C22×D11—21no—
112C22×D11—21no—
113C22×D11—21no—
114C22×D11—21no—
115C22×D11—21no—
116C22×D11—21no—
117C22×D11—21no—
118C22×D11—21no—
119C22×D11—21no—
120C22×D11C2×D412yes—
121Q8×C11—44no—
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11—21no—
126C2×C4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11—21no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11—21no—
134C2×C4×C11—21no—
135C2×C4×C11—21no—
136C2×C4×C11—21no—
137C2×C4×C11—21no—
138C2×C4×C11—21no—
139C2×C4×C11—21no—
140C2×C4×C11—21no—
141C2×C4×C11C2×D412yes—
142C2×C4×C11C2×D412yes—
143C2×Dic11—21no—
144C2×Dic11—21no—
145C2×Dic11—21no—
146C2×Dic11—21no—
147C2×Dic11—21no—
148C2×Dic11—21no—
149C2×Dic11—21no—
150C2×Dic11—21no—
151C2×Dic11—21no—
152C2×Dic11—21no—
153C2×Dic11—21no—
154C2×Dic11—21no—
155C2×Dic11—21no—
156C2×Dic11—21no—
157C2×Dic11C2×D412yes—
158C2×Dic11C2×D412yes—
159C2×Dic11C2×D412yes—
160C2×Dic11#4112yes—
161D44—44no—
162C4×D11—44no—
163Dic22—44no—
164C2×C4⋊Q8—111no—
165C2×#124—111no—
166C2×#123—111no—
167C2×C22⋊Q8—111no—
168#399—111no—
169#397—111no—
170#396—111no—
171#395D1111yescharacteristic, complemented
172#394—111no—
173#393—111no—
174#389—111no—
175#388—111no—
176#388—111no—
177#387—111no—
178#385—111no—
179C22×C11C22×D411yescharacteristic
180C22×C11C22×D411yescharacteristic
181C22×C11C2×#4111yescharacteristic
182C22×C11H(5,𝔽2)11yescharacteristic
183C22×C112−1+411yescharacteristic
184C22×C112−1+411yescharacteristic
185C22×C112−1+411yescharacteristic
186C2×D11—22no—
187C2×D11—22no—
188C2×D11—22no—
189C2×D11—41no—
190C2×D11—41no—
191C2×D11—41no—
192C2×D11—41no—
193C2×D11—41no—
194C2×D11—41no—
195C2×D11—41no—
196C2×D11—41no—
197C2×D11—41no—
198C2×D11—41no—
199C2×D11—41no—
200C4×C11—22no—
201C4×C11—22no—
202C4×C11—41no—
203C4×C11—41no—
204C4×C11—41no—
205C4×C11—41no—
206C4×C11—41no—
207Dic11—22no—
208Dic11—22no—
209Dic11—22no—
210Dic11—22no—
211Dic11—41no—
212Dic11—41no—
213C22×Q8—111no—
214C22×Q8C2×D1111yescharacteristic
215C22×D4—111no—
216C23×C4—111no—
217C4⋊Q8—224no—
218#124—224no—
219#123—224no—
220C22⋊Q8—224no—
221C2×C4⋊C4—111no—
222C2×C4⋊C4—111no—
223C2×C4⋊C4—111no—
224C2×C4⋊C4—111no—
225C2×C4⋊C4—111no—
226C2×C4⋊C4—111no—
227C2×C4⋊C4—111no—
228C2×C4⋊C4C2×D1111yescharacteristic
229C2×C4⋊C4C2×D1111yescharacteristic
230C2×C4⋊C4C2×D1111yescharacteristic
231C2×C22⋊C4—111no—
232C2×C22⋊C4—111no—
233C2×C22⋊C4—111no—
234C2×C22⋊C4—111no—
235C2×C22⋊C4—111no—
236C2×C22⋊C4—111no—
237C2×C22⋊C4—111no—
238C2×C22⋊C4—111no—
239C2×C22⋊C4—111no—
240C2×C22⋊C4—111no—
241C2×C22⋊C4—111no—
242C2×C42—111no—
243C2×C42—111no—
244#95—111no—
245#95—111no—
246#95—111no—
247#95—111no—
248#95—111no—
249#95C2×D1111yescharacteristic
250#95C2×D1111yescharacteristic
251#95C2×D1111yescharacteristic
252C2×C11#53611yescharacteristic
253C2×C11#53611yescharacteristic
254C2×C11#54211yescharacteristic
255C2×C11D4211yescharacteristic
256C2×C11#54711yescharacteristic
257C2×C11#54811yescharacteristic
258C2×C11#56311yescharacteristic
259D11—42no—
260D11—81no—
261C24—111no—
262C24—111no—
263C2×Q8—22no—
264C2×Q8—22no—
265C2×Q8—41no—
266C2×Q8—222no—
267C2×Q8—222no—
268C2×Q8—441no—
269C2×D4—222no—
270C2×D4—222no—
271C2×D4—441no—
272C22×C4—111no—
273C22×C4—111no—
274C22×C4—111no—
275C22×C4—111no—
276C22×C4—111no—
277C22×C4—111no—
278C22×C4—222no—
279C22×C4—222no—
280C22×C4—441no—
281C22×C4C22×D1111yescharacteristic
282C22×C4C22×D1111yescharacteristic
283C22×C4C22×D1111yescharacteristic
284C22×C4C22×D1111yescharacteristic
285C22×C4C22×D1111yescharacteristic
286C22×C4C22×D1111yescharacteristic
287C22×C4C22×D1111yescharacteristic
288C4⋊C4—22no—
289C4⋊C4—22no—
290C4⋊C4—41no—
291C4⋊C4—114no—
292C4⋊C4—222no—
293C4⋊C4—222no—
294C4⋊C4—222no—
295C4⋊C4—222no—
296C4⋊C4—222no—
297C4⋊C4—222no—
298C22⋊C4—114no—
299C22⋊C4—222no—
300C22⋊C4—222no—
301C22⋊C4—222no—
302C22⋊C4—222no—
303C22⋊C4—222no—
304C22⋊C4—222no—
305C22⋊C4—222no—
306C22⋊C4—222no—
307C22⋊C4—222no—
308C22⋊C4—441no—
309C42—222no—
310C42—222no—
311C11#267411yescharacteristic, complemented, Sylow
312C23—112no—
313C23—221no—
314C23—221no—
315C23—221no—
316C23—221no—
317C23—221no—
318C23—221no—
319C23—221no—
320C23—221no—
321C23—221no—
322C23—221no—
323C23—221no—
324C23—221no—
325C23—221no—
326C23C23×D1111yescharacteristic
327Q8—44no—
328Q8—444no—
329D4—444no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—112no—
350C2×C4—112no—
351C2×C4—112no—
352C2×C4—112no—
353C2×C4—221no—
354C2×C4—221no—
355C2×C4—221no—
356C2×C4—221no—
357C2×C4—221no—
358C2×C4—221no—
359C2×C4—221no—
360C2×C4—221no—
361C2×C4—221no—
362C2×C4—221no—
363C2×C4—221no—
364C2×C4—221no—
365C2×C4—221no—
366C2×C4—221no—
367C2×C4—444no—
368C2×C4D4×D1112yes—
369C2×C4D4×D1112yes—
370C22—222no—
371C22—222no—
372C22—222no—
373C22—441no—
374C22—441no—
375C22—441no—
376C22—441no—
377C22—441no—
378C22—441no—
379C22—441no—
380C22—441no—
381C22—441no—
382C22—441no—
383C22—441no—
384C22C2×D4×D1111yescharacteristic
385C22C2×D4×D1111yescharacteristic
386C22#6703711yescharacteristic
387C22#6704011yescharacteristic
388C22#6704011yescharacteristic
389C22#6704011yescharacteristic
390C22#41×D1111yescharacteristic
391C4—22no—
392C4—22no—
393C4—41no—
394C4—41no—
395C4—41no—
396C4—41no—
397C4—41no—
398C4—222no—
399C4—222no—
400C4—222no—
401C4—222no—
402C4—441no—
403C4—441no—
404C2—442no—
405C2—881no—
406C2#1062312111yescharacteristic
407C2#1062316211yescharacteristic
408C2#1062316411yescharacteristic
409C2#1062317111yescharacteristic
410C2#1062325511yescharacteristic
411C2#1062325511yescharacteristic
412C2#1062326611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#395C2
prime radicalC22×D44C22
hypercenter#395D11
hypocenterC11#2674
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #395

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×#66997C2semidirect
3. C2×#66949C2semidirect
5. C11×#395C2semidirect
6. #10622605C2semidirect
7. #10622603C2semidirect
8. #10622602C2semidirect
9. #10622585C2semidirect
10. #10622289C2semidirect
11. #10622288C2semidirect
12. #10622286C2semidirect
14. #10622282C2semidirect
15. #10622265C2semidirect
171. #395D11semidirect
311. C11#2674semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#670002
C2×#669972
C2×#669492
C2×#669472
C11×#3952
#106226052
#106226032
#106226022
#106225852
#106222892
#106222882
#106222862
#106222852
#106222822
#106222652
#267411